1
MCQ (More than One Correct Answer)

JEE Main 2016 (Online) 10th April Morning Slot

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?
A
A2 $$-$$ B2C2
B
$${{\left( {A - C} \right)} \over D}$$
C
$${A \over B} - C$$
D
$${C \over {BD}} - {{A{D^2}} \over C}$$

Explanation

Given,

AD = c ln (BD)

As log is dimensionless.

So, [BD] = 1   $$ \Rightarrow $$  [B] = $${1 \over {\left[ D \right]}}$$

And  [AD] = [C]

Now checking options one by one

(a)   [B2 C2] = [B2] [A2 D2] = [A2] [B2 D2] = [A2]

$$ \therefore $$   This is meaningful.

(b)   $$\left( {{{A - C} \over D}} \right)$$ is not meaningful.

As dimension of A $$ \ne $$ dimension of C

Hence (A $$-$$ C)   is not possible.

(c)   $$\left[ {{A \over B}} \right]$$ = [AD] = [C]

$$ \therefore $$   $${{A \over B}}$$ $$-$$ C is meaningful.

(d)   $$\left[ {{C \over {BD}}} \right]$$ = $${{\left[ C \right]} \over {\left[ {BD} \right]}}$$ = $${{\left[ C \right]} \over 1}$$ = [C]

$$\left[ {{{A{D^2}} \over C}} \right]$$ = $${{\left[ {AD} \right]\left[ D \right]} \over {\left[ C \right]}}$$ = $${{\left[ C \right]\left[ D \right]} \over {\left[ C \right]}}$$ = [D]

As dimension of C and D are not same so it is not meaning ful.

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